Rendering Geometric Shapes Using Volumetric Constructive Solid Geometry
Hieu Quang Tran
Faculty Advisor: Professor Douglas Baldwin
Computer Science Department, State University of New York at Geneseo
Funded by the Laboratory for Laser Enegertics at the University of Rochester
Constructive Solid Geometry
A technique used to create complex three dimensional geometric shapes by applying Boolean operations on primitive shapes.
This project tests the hypothesis that CSG can be rendered quickly and with good image quality by suitably creating and using three-dimensional texture maps.
Three Dimensional Texture Mapping
Sampling Line Tracing
The texture map contains voxels storing opacity information: voxels By tracing sampling lines through the CSG model, we can easily idenoutside the model have alpha values of zero (transparent) and voxels tify which voxels are transparent, which voxels are opaque.
inside the model have alpha values of one (opaque).
Positive and Negative Surfaces
Sampling Line Sharing
To improve the image quality, we shrink triangles of surfaces that are Sampling lines are traced along edges, faces, and through the centers
inside the model (positive surfaces) and expand triangles of surfaces of columns of voxels, allowing sampling lines to be shared between
adjacent voxels.
whose complements are inside the model (negative surfaces).
Quad Tree
Columns of voxels are grouped into nodes of a quad tree in the dimensions perpendicular
to the columns. This grouping allows us to quickly identify tree nodes that do not contain
any primitives and therefore do not need to have sampling lines traced through their voxels.
Results
We evaluate the image quality of Volumetric CSG and measure its preprocessing time in comparison with Triangle Subdivision, an alternative
technique to volumetric CSG. In conclusion, Volumetric CSG shows great improvement on preprocessing time and produces reasonable image quality. In the future, we want to further improve the image quality produced by Volumetric CSG and characterize its rendering speed.
50HCrack
Half Space
Yag_in